Problem: A group of adults and kids went to see a movie. Tickets cost $$5.50$ each for adults and $$3.50$ each for kids, and the group paid $$50.00$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${5.5x+3.5y = 50}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${5.5}{(y-4)}{+ 3.5y = 50}$ Simplify and solve for $y$ $ 5.5y-22 + 3.5y = 50 $ $ 9y-22 = 50 $ $ 9y = 72 $ $ y = \dfrac{72}{9} $ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(8)}{ - 4}$ ${x = 4}$ You can also plug ${y = 8}$ into ${5.5x+3.5y = 50}$ and get the same answer for $x$ ${5.5x + 3.5}{(8)}{= 50}$ ${x = 4}$ There were $4$ adults and $8$ kids.